Parabola questions
264 published questions with worked solutions.
- Let S be the focus of the parabola y^2 = 8x and let PQ be the common chord of the circle x^2 + y^2 - 2x - 4y = 0 and the given...
- If the normals of the parabola y^2=4x drawn at the end points of its latus rectum are tangents to the circle (x-3)^2+(y+2)^2=r^2,...
- Let P and Q be distinct points on the parabola y^2=2x such that a circle with PQ as diameter passes through the vertex O of the...
- Suppose that the foci of the ellipse x^2 9 + y^2 5 =1 are (f_1,0) and (f_2,0) where f_1>0 and f_2<0. Let P_1 and P_2 be two...
- If a chord, which is not a tangent, of the parabola y^2=16x has the equation 2x+y=p, and midpoint (h,k), then which of the...
- If x^2 + 6x + 20y - 51 = 0, then axis of parabola is
- Equation of tangent to the parabola y^2 = 16x at P(4, 8) is
- The equation of parabola with focus (0, 0) and directrix x + y = 4, is
- The point of the parabola y^2 = 18x, for which the ordinate is three times the abscissa is
- From the point (-1, -6) two tangents are drawn to the parabola y^2 = 4x. Then, the angle between the two tangents is
- The equation of the directrix of (x - 1)^2 = 2(y - 2) is
- If (-1, -2 2 ) is one of extremity of a focal chord of the parabola y^2 = -8x, then the other extremity is
- The equation of the parabola with vertex at the origin and directrix y = 2 is
- Equation of the directrix of parabola 2x^2 = 14y is equal to
- The conditions that ax + by + c = 0 is tangent to the parabola y^2 = 4ax, is
- The focus of the parabola y^2 - x - 2y + 2 = 0 is
- The length intercepted by the curve y^2 = 4x on the line satisfying dy/dx = 1 and passing through point (0, 1), is given by
- Axis of a parabola is y = x and vertex and focus are at a distance 2 and 2 2 respectively from the origin. Then, equation of the...
- The vertex of the parabola x^2 + 2y = 8x - 7 is
- Equation of the parabola with its vertex at (1, 1) and focus (3, 1) is
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